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S3-covers of Schemes

Published online by Cambridge University Press:  20 November 2018

Robert W. Easton
Robert W. Easton*
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA email: [email protected]
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Abstract

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We analyze flat ${{S}_{3}}$-covers of schemes, attempting to create structures parallel to those found in the abelian and triple cover theories. We use an initial local analysis as a guide in finding a global description.

Keywords

14L30nonabelian groupspermutation groupgroup coversschemes
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 5 , 18 October 2011 , pp. 1058 - 1082
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Abelson, H., Topologically distinct conjugate varieties with finite fundamental group. Topology 13(1974), 161–176. doi:10.1016/0040-9383(74)90006-8Google Scholar
[2] A, F.. Bogomolov, Holomorphic tensors and vector bundles on projective varieties. Math. USSR-Izv. 13(1979), 499–555.Google Scholar
[3] Bolognesi, M. and A. Vistoli, Stacks of trigonal curves. Preprint (Mar. 2009), arxiv:0903.0965.Google Scholar
[4] Catanese, F., On the moduli space of surfaces of general type. J. Differential Geom. 19(1984), 483–515.Google Scholar
[5] Catanese, F., Connected components of moduli spaces. J. Differential Geom. 24(1986), 395–399.Google Scholar
[6] Easton, R., Surfaces violating Bogomolov–Miyaoka–Yau in positive characteristic. Proc. Amer. Math. Soc. 136(2008), 2271–2278. doi:10.1090/S0002-9939-08-09466-5Google Scholar
[7] Easton, R., S -covers of schemes. PhD thesis, Stanford University, 2007.Google Scholar
[8] Easton, R. and R. Vakil, Absolute Galois acts faithfully on the components of the moduli space of surfaces: 3 A Belyi-type theorem in higher dimension. Int. Math. Res. Not. 2007(2007). Article ID rnm080, 10 pages, doi:10.1093/imrn/rnm080.Google Scholar
[9] Eisenbud, D., Commutative algebra with a view towards algebraic geometry. Springer-Verlag, New York, 1995.Google Scholar
[10] Hahn, D. and R. Miranda, Quadruple covers in algebraic geometry. J. Algebraic Geom. 8(1999), 1–30.Google Scholar
[11] Hartshorne, R., Algebraic geometry. Springer, 1977.Google Scholar
[12] Hirzebruch, F., Arrangements of lines and algebraic surfaces. In: Arithmetic and Geometry, Vol. II, Progr. Math. 36(1983), 113–140.Google Scholar
[13] Jacobson, N., Basic Algebra I. W. H. Freeman and Co., San Francisco, CA, 1974.Google Scholar
[14] E, W.. Lang, Examples of surfaces of general type with vector fields. In: Arithmetic and Geometry, Vol. II, Progr. Math. 36(1983), 167–173.Google Scholar
[15] Matsumura, H., Commutative algebra. Second edition, Mathematics Lecture Note Series 56, Benjamin-Cummings Pub. Co., 1980.Google Scholar
[16] Miranda, R., Triple covers in algebraic geometry. Amer. J. Math. 107(1985), 1123–1158. doi:10.2307/2374349Google Scholar
[17] Miyaoka, Y., On the Chern numbers of surfaces of general type. Invent. Math. 42(1977), 225–237. doi:10.1007/BF01389789Google Scholar
[18] Mumford, D., Geometric invariant theory. Third edition, Springer-Verlag, Berlin, 1994.Google Scholar
[19] Pardini, R., Abelian covers of algebraic varieties. J. Reine Angew. Math. 417(1991), 191–213. doi:10.1515/crll.1991.417.191Google Scholar
[20] Pardini, R., Triple covers in positive characteristic. Ark. Mat. 27(1989), 319–341. doi:10.1007/BF02386379Google Scholar
[21] Rotman, J., Advanced Modern Algebra. Pearson Education, Inc., 2002.Google Scholar
[22] Tokunaga, H., On dihedral Galois coverings. Canad. J. Math. 46(1994), 1299–1317. doi:10.4153/CJM-1994-074-4Google Scholar
[23] Tokunaga, H., Dihedral coverings of algebraic surfaces and their applications. Trans. Amer. Math. Soc. 352(2000), 4007–4017. doi:10.1090/S0002-9947-00-02524-1Google Scholar
[24] Tokunaga, H., Galois covers of S and their applications. Osaka J. Math. 39(2002), 621–645.Google Scholar
[25] Tokunaga, H., Triple coverings of algebraic surfaces according to the Cardano formula. J. Math. Kyoto Univ. 4 and A 4 31(1991), 359–375.Google Scholar
[26] Yau, S.-T., The Calabi conjecture and some new results in algebraic geometry. Proc. Natl. Acad. Sci. USA 74(1977), 1798–1799. doi:10.1073/pnas.74.5.1798Google Scholar
[27] Zariski, O., On the purity of the branch locus of algebraic functions. Proc. Natl. Acad. Sci. USA 44(1958), 791–796. doi:10.1073/pnas.44.8.791Google Scholar